Abstract
In this paper, a new mathematical model for Pennes’ bioheat equation using the new memory-dependent derivative is established. The one-dimensional thermal behavior in living tissue subject to instantaneous surface heating is investigated. Numerical calculations are performed to study the temperature transients in the skin exposed to instantaneous surface heating. Numerical results are plotted in the form of two-dimensional graphs and discussed. In this novel model, the time delay parameter is a new indicator of bio-heat efficiency in living tissues.
Highlights
The memory-dependent derivative is defined in an integral form of a common derivative with a Kernel function on a slipping interval [1]
The time delay parameter is a new indicator of bio-heat efficiency in living tissues
The memory-dependent derivative is successfully incorporated into a bioheat transfer model
Summary
The memory-dependent derivative is defined in an integral form of a common derivative with a Kernel function on a slipping interval [1] This kind of definition is better than the fractional one for reflecting the memory effect (instantaneous change rate depends on the past state). The first order memory-dependent derivative of a function ( ) was introduced by Wang and Li [1] They defined it in an integral form of a common derivative with a Kernel of function on slipping interval in the form:. Numerical results are plotted in the form of two-dimensional graphs and discussed In this novel model, the time delay parameter is a new indicator of bio-heat efficiency in living tissues
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